A gis represents reality, it is not reality a gis represents reality, it is not reality


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A GIS represents reality, it is not reality.

  • A GIS represents reality, it is not reality.

  • A GIS map must accurately represent feature locations.

  • To determine location of features in real world or on map need a reference system

    • A set of lines of known location that can be used to determine the locations of features that fall between the lines


Coordinate Systems

  • Coordinate Systems

    • Reference systems used to determine feature locations
  • In this module learn about

    • different coordinate systems
    • how they work
    • how to change the coordinate system of a map.
  • Understanding coordinate systems  manage your data to increase accuracy



Name two types of coordinate systems.

  • Name two types of coordinate systems.

  • Identify components of each type of coordinate system.

  • Assign coordinate system information to a dataset.

  • Set display units for a data frame and measure distances on a map.

  • Explain what a map projection is.

  • List the major categories of map projections.

  • List spatial properties that may be distorted when different map projections are applied.

  • Change the map projection for a data frame and describe its effects.



Two types of coordinate systems

  • Two types of coordinate systems

    • Geographic
      • Used to locate objects on the curved surface of the earth
    • Projected
      • Used to locate objects on a flat surface
        • a paper map or a digital GIS map displayed on a flat computer screen.
  • Each attempts to model earth and feature locations accurately

    • But no system is completely accurate


Reference system for identifying locations and measuring features on the curved surface of the earth

  • Reference system for identifying locations and measuring features on the curved surface of the earth

  • Consists of a network of intersecting lines called a graticule

    • Intersecting lines = longitude and latitude


Graticule

  • Graticule

    • Longitude
      • Vertical lines
    • Latitude
    • Horizontal lines
  • Because earth is spherical, these lines form circles



Measurements expressed in

  • Measurements expressed in

    • Degrees
      • 1/360th of a circle.
      • Can be divided into 60 minutes
    • Minutes
      • Can be divided into 60 seconds
    • Seconds


Lines of longitude

  • Lines of longitude

    • Called meridians
    • Measures of longitude begin at the prime meridian
      • Defines zero value for longitude
    • Range from 0° to 180° going east
    • Range from 0° to -180° going west


Prime meridian

  • Prime meridian

    • Green line
    • Starting point for longitude
    • Has a value of 0
  • Equator

    • Red line
    • Starting point for latitude
    • Has a value of 0
    • Runs midway between the north and south poles
      • Dividing earth into northern and southern hemispheres.


Longitude and latitude actually angles measured from earth's center to point on earth's surface

  • Longitude and latitude actually angles measured from earth's center to point on earth's surface

  • For example, consider these coordinates:

    • Longitude: 60 degrees East (60° 00' 00")
    • Latitude: 55 degrees, 30 minutes North (55° 30' 00")
  • Longitude coordinate refers to angle formed by two lines

    • one at the prime meridian
    • the other extending east along the equator.
  • Latitude coordinate refers to angle formed by two lines

    • one on the equator
    • the other extending north along the 60° meridian.


Longitude and latitude are angles measured from the earth's center to a point on the earth's surface.

  • Longitude and latitude are angles measured from the earth's center to a point on the earth's surface.



Many models of the earth's shape

  • Many models of the earth's shape

    • Each has its own geographic coordinate system
  • All based on

    • degrees of latitude and longitude
  • Exact latitude-longitude values assigned to individual locations will vary



Two shapes commonly used to model earth

  • Two shapes commonly used to model earth

    • Sphere
    • Spheroid


Assuming the earth is a sphere greatly simplifies mathematical calculations

  • Assuming the earth is a sphere greatly simplifies mathematical calculations

    • Works well for small-scale maps
      • Maps that show large area of the earth
  • A sphere does not provide enough accuracy for large-scale maps

    • maps that show smaller area of earth in more detail
  • For those, it is preferable to use a spheroid

  • A spheroid is a more accurate model of the earth, but it's not perfect.



Planet Earth

  • Planet Earth

    • slightly pear-shaped and bumpy
    • has several dents and undulations
    • south pole is closer to the equator than north pole
  • Geoid

    • Model for complicated of earth
    • Too mathematically complicated to use for practical purposes, so spheroid is used as a compromise


Different spheroids currently in use

  • Different spheroids currently in use

  • Some spheroids were developed to

    • Model the entire earth
    • Model specific regions more accurately
  • World Geodetic System of 1972 (WGS72) and 1984 (WGS84)

    • Used to represent the whole world
  • Clarke 1866 and Geodetic Reference System of 1980 (GRS80)

    • Most commonly used in North America


Why do you need to know about spheroids?

  • Why do you need to know about spheroids?

    • Because ignoring deviations and using the same spheroid for all locations on the earth could lead to measurement errors of several meters or, in extreme cases, hundreds of meters.


A spheroid doesn't describe the earth's shape exactly.

  • A spheroid doesn't describe the earth's shape exactly.

  • A geographic coordinate system needs a way to align the spheroid being used to the surface of the earth for the region being studied.

  • For this purpose, a geographic coordinate system uses a datum.

    • A datum specifies which spheroid you are using as your earth model and at which exact location (a single point) you are aligning that spheroid to the earth's surface.


Red spheroid

  • Red spheroid

    • Aligned to the earth to preserve accurate measurements for North America
  • Blue spheroid

    • Aligned to the earth to preserve accurate measurements for Europe


Datum

  • Datum

    • Defines origin of geographic coordinate system
      • The point where the spheroid matches up perfectly with the surface of the earth and where the latitude-longitude coordinates on the spheroid are true and accurate.
    • All other points in the system are referenced to the origin.
    • In this way, a datum determines how your geographic coordinate system assigns latitude-longitude values to feature locations.
  • There are different datums to help align the spheroid to the surface of the earth in different regions



If you change the datum of the geographic coordinate system, you should know that the coordinate values of your data will also change.

  • If you change the datum of the geographic coordinate system, you should know that the coordinate values of your data will also change.

  • For example, consider a location in Redlands, California, that is based on the North American Datum of 1983

    • The coordinate values of this location are:
      • –117° 12' 57.75961" (longitude) 34° 01' 43.77884" (latitude)
  • Now consider the same point on the North American Datum of 1927

      • –117° 12' 54.61539" (longitude) 34° 01' 43.72995" (latitude)
  • The longitude value differs by about three seconds, while the latitude value differs by about 0.05 seconds.



In both NAD 1927 and the NAD 1983 datums

  • In both NAD 1927 and the NAD 1983 datums

    • Spheroid matches the earth closely in North America
    • Is quite a bit off in other areas
  • Notice that the datums use different spheroids and different origins

  • NAD 1927

    • origin aligns the Clark 1866 spheroid with a point in North America
  • NAD 1983

    • Origin aligns the center of the spheroid with the center of the earth


The most recently developed and widely used datum for locational measurement worldwide is

  • The most recently developed and widely used datum for locational measurement worldwide is

    • World Geodetic System of 1984 (WGS 1984)


The surface of the earth is curved but maps are flat.

  • The surface of the earth is curved but maps are flat.

  • To convert feature locations from the spherical earth to a flat map

    • Latitude and longitude coordinates from a geographic coordinate system must be converted, or projected, to planar coordinates


A map projection uses mathematical formulas to convert geographic coordinates on the spherical globe to planar coordinates on a flat map.

  • A map projection uses mathematical formulas to convert geographic coordinates on the spherical globe to planar coordinates on a flat map.



Projected coordinate system

  • Projected coordinate system

    • A reference system for identifying locations and measuring features on a flat (map) surface
    • Consists of lines that intersect at right angles, forming a grid
    • Based on Cartesian coordinates
      • Have an origin, an x and a y axis, and a unit for measuring distance


Based on Cartesian coordinates which use a grid.

  • Based on Cartesian coordinates which use a grid.

  • Feature locations are measured using x and y coordinate values from the point of origin.



The origin of the projected coordinate system

  • The origin of the projected coordinate system

    • (0,0)
    • commonly coincides with the center of the map.
  • This means that x and y coordinate values will be positive only in one quadrant of the map (the upper right).

    • On published maps, however, it is desirable to have all the coordinate values be positive numbers.


To offset this problem

  • To offset this problem

    • Mapmakers add 2 numbers to each x and y value
    • Numbers are big enough to ensure that all coordinate values, at least in the area of interest, are positive values.
    • False easting
      • Number added to the x coordinate
    • False northing
      • Number added to the y coordinate


A false easting value of 7,000,000 was added to each x coordinate.

  • A false easting value of 7,000,000 was added to each x coordinate.

  • A false northing value of 2,000,000 was added to each y coordinate.



All geographic datasets have a geographic coordinate system (GCS).

  • All geographic datasets have a geographic coordinate system (GCS).

  • Some datasets also have a projected coordinate system (PCS).

  • When you add a dataset to ArcMap it detects the geographic coordinate system and the projected coordinate system if there is one



If all the data you want to display on a map is stored in the same geographic coordinate system, you can just add it to the map—the layers will overlay properly.

  • If all the data you want to display on a map is stored in the same geographic coordinate system, you can just add it to the map—the layers will overlay properly.

  • If some of the datasets also have projected coordinate systems, even if they are different, you can also just add them to the map without data alignment worries—

  • ArcMap will automatically make the layers overlay using a process called "on-the fly projection."

  • The geographic coordinate system is the common language.

  • ArcMap can convert the geographic coordinate system to any projected coordinate system and it can convert any projected coordinate system back to the geographic coordinate system.



An issue arises when you want to display datasets that have different geographic coordinate systems on the same map.

  • An issue arises when you want to display datasets that have different geographic coordinate systems on the same map.

  • The first layer you add to an empty data frame determines the coordinate system for the data frame.

  • If that layer has a projected coordinate system, the data frame will have that same projected coordinate system.

  • If you add a layer that has the same geographic coordinate system but a different projected coordinate system (or no projected coordinate system at all), ArcMap will perform an on-the-fly projection and convert the data to the data frame's projected coordinate system.

  • The layers will overlay properly.



If, however, you try to add a layer that has a different geographic coordinate system, ArcMap will display a warning message telling you that it may not be able to properly align the data.

  • If, however, you try to add a layer that has a different geographic coordinate system, ArcMap will display a warning message telling you that it may not be able to properly align the data.

  • ArcMap can still project the data on the fly, but it can no longer guarantee perfect alignment.

    • For perfect data alignment, you need to apply a transformation to make the geographic coordinate systems match


How do you know what coordinate system your data is stored in?

  • How do you know what coordinate system your data is stored in?

    • You can view the coordinate system information for a dataset in ArcCatalog™, in its metadata.
    • If a dataset has no coordinate system information in its metadata (it's missing), you may not be able to display the data in ArcMap.
    • You may need to do some research to find out the coordinate system, then define the coordinate system using the ArcGIS tools provided.


Map units

  • Map units

    • Units in which coordinates for a dataset are stored
    • Determined by the coordinate system
    • If data is stored in a geographic coordinate system
      • Map units are usually decimal degrees
    • If data is stored in a projected coordinate system
      • Map units are usually meters or feet
    • Units can be changed only by changing the data's coordinate system.
  • Display unit

    • Independent of map units
    • Are a property of a data frame
    • The units in which ArcMap displays coordinate values and reports measurements.
    • You can set the display units for any data frame and change them at any time.


Latitude and longitude are angle measurements

  • Latitude and longitude are angle measurements

  • Angles are measured in degrees.

  • Degrees can be expressed two ways:

    • degrees, minutes, seconds (DMS)
    • decimal degrees (DD).
  • In a GIS, decimal degrees are more efficient because they make digital storage of coordinates easier and computations faster.



View and modify coordinate system information

  • View and modify coordinate system information



Map projection

  • Map projection

    • Used to convert data from a geographic coordinate system to a projected (planar) coordinate system
  • There are many different map projections

    • Each preserves the spatial properties of data (shape, area, distance, and direction) differently


Maps are always flat, so do you always need a map projection?

  • Maps are always flat, so do you always need a map projection?

    • Maybe—it depends on what you want to do.
  • For example, suppose your project doesn't require a high level of locational accuracy—you won't be performing analysis based on location and distance or you just want to make a quick map. In these situations, there is probably no need to convert your data to a projected coordinate system.



Use a map projection to convert data to a projected coordinate system

  • Use a map projection to convert data to a projected coordinate system

    • If you need to perform analysis
      • measure distances, calculate areas and perimeters, determine the shortest route between two points
    • If you need to show a particular spatial property for features on a map as it really exists on the earth


The term "map projection" comes from the concept of projecting a light source through the earth's surface onto a two-dimensional surface (a map).

  • The term "map projection" comes from the concept of projecting a light source through the earth's surface onto a two-dimensional surface (a map).



Map projections are created using mathematical formulas

  • Map projections are created using mathematical formulas

  • There are three types of surfaces that a map can be projected onto:

    • Cylinder
    • Cone
    • Plane
  • Each of these surfaces can be laid flat without distortion.



Projections based on each surface can be used for mapping particular parts of the world

  • Projections based on each surface can be used for mapping particular parts of the world

  • Cylinder

    • wrapped around the earth so that it touches the equator
    • accurate in the equatorial zone
  • Cone

  • Plane

    • touches the earth at a pole
    • accurate in the polar region.
  • Knowing the surface used helps determine if the map projection is right for purpose



Produce maps with

  • Produce maps with

    • straight, evenly-spaced meridians
    • straight parallels that intersect meridians at right angles
  • Created by

    • wrapping a cylinder around a globe
    • projecting a light source through the globe onto the cylinder
    • cutting along a line of longitude
    • Being laid flat


Produce maps with

  • Produce maps with

    • straight converging longitude lines
    • concentric circular arcs for latitude lines
  • Created by

    • setting a cone over a globe
    • projecting light from the center of the globe onto the cone
    • cutting along a longitude line


Produce maps on which

  • Produce maps on which

    • longitude lines converge at the north pole and radiate outward
    • Latitude lines appear as a series of concentric circles
  • Created by

    • passing a light source through the earth onto a flat surface (plane).
    • In this example, the plane touches the earth at the north pole.


Converting locations from a spherical surface to a flat surface causes distortion

  • Converting locations from a spherical surface to a flat surface causes distortion

  • Four spatial properties subject to distortion:

    • Shape
    • Area
    • Distance
    • Direction
  • Each map projection is good at preserving one or more (but not all)



Different map projections preserve different spatial properties and produce different-looking maps.

  • Different map projections preserve different spatial properties and produce different-looking maps.



Shape

  • Shape

    • Shapes, such as outlines of countries, look the same on the map as they do on the earth.
    • Called "conformal”
    • Compass directions are true for a limited distance around any given location


Area

  • Area

    • Size of a feature on the map is the same relative to its size on the earth
    • If you draw a shape and move it around the map, no matter where you place it, its size will be the same


Distance

  • Distance

    • A line between one point on the map and another is the same distance as it is on the earth (taking scale into consideration).
    • Most maps have one or two lines of true scale.
    • An equidistant map preserves true scale for all straight lines passing through a single specified location
      • i.e. if the map is centered on Moscow, a linear measurement from Moscow to any other point on the map would be correct


Direction

  • Direction

    • Direction, or azimuth, is measured in degrees of angle from north
    • preserves direction for all straight lines passing through a single, specified location
    • Directions from one central location to all other points on the map will be shown correctly


The azimuth from A to B is 22 degrees. If the azimuth value from A to B is the same on a map as it is on the earth, then the map preserves direction from A to B.

  • The azimuth from A to B is 22 degrees. If the azimuth value from A to B is the same on a map as it is on the earth, then the map preserves direction from A to B.



Anyone who uses maps should know which projections are being used and which spatial properties are distorted and to what extent.

  • Anyone who uses maps should know which projections are being used and which spatial properties are distorted and to what extent.

  • When choosing a map projection, think about which properties you want to preserve.

    • If your map is large-scale (shows a relatively small area of the earth), the effect of a map projection will be much less than if your map is small-scale (shows a large portion of the earth's surface).


Which map projection you choose for a particular map depends on

  • Which map projection you choose for a particular map depends on

    • Map's purpose
    • Spatial properties you want to preserve


If map will be used for general reference or in an atlas

  • If map will be used for general reference or in an atlas

    • Want to balance shape and area distortion.
    • In this case, a compromise projection such as the Robinson projection may be the best choice.
  • If map has a specific purpose

    • May need to use a projection that preserves a specific spatial property




Other factors to consider when choosing a map projection

  • Other factors to consider when choosing a map projection

    • the size of the area you're mapping,
    • the orientation (east-west or north-south)
    • the particular portion of the earth that is covered.
  • When working at a large scale

    • distortion doesn't play a big role
    • almost any projection centered on your area will be appropriate
  • In some situations, decision of which map projection to use has already been made

    • State Plane and UTM are standard for mapping U.S. states


Compare different map projections

  • Compare different map projections



All geographic datasets have a geographic coordinate system (GCS).

  • All geographic datasets have a geographic coordinate system (GCS).

  • There are different spheroids for different parts of the world, and there are different datums to help align the spheroid with the surface of the earth in different regions.

  • As long as they have a common geographic coordinate system, ArcMap can properly display multiple datasets in the same data frame using a process called "on-the-fly projection."



In ArcMap, the first layer you add to an empty data frame sets the coordinate system for the data frame.

  • In ArcMap, the first layer you add to an empty data frame sets the coordinate system for the data frame.

  • You should use a map projection when you need to perform analysis, take accurate measurements, or when you need to show a particular spatial property as it really exists on the earth.

  • Anyone who uses maps should know which projections are being used and which properties are distorted and to what extent.



What are the components of a geographic coordinate system?

  • What are the components of a geographic coordinate system?

  • Name one way you can get information about the coordinate system of a dataset in ArcCatalog.

  • What are the two most important factors to consider when choosing a map projection?



A geographic coordinate system is defined by a prime meridian (usually Greenwich), a datum (which includes a spheroid), and an angular unit of measure (degrees).

  • A geographic coordinate system is defined by a prime meridian (usually Greenwich), a datum (which includes a spheroid), and an angular unit of measure (degrees).

  • You can use the Metadata tab to view the coordinate system information for a dataset. You can also look at the dataset's Properties dialog box.

  • When choosing a map projection, you should consider the purpose of the map and which spatial properties you want to preserve.




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